Just tried updating my password for my weebly account. It appears this functionality is broken. It keeps telling me that "Your current password must be correct". I logged in and out with the same password a couple times to confirm I'm not crazy.
Can you email me at david@weebly.com? We looked into this shortly after you posted this comment and can't replicate (also not receiving other complaints)... If you can email me we'll get to the bottom of it -- thanks for letting us know!